Answer:
0.28 yr
Step-by-step explanation:
To find the doubling time with continuous compounding, we should look at the formula:
[tex]FV = PVe^{rt}[/tex]
FV = future value, and
PV = present value
If FV is twice the PV, we can calculate the doubling time, t
[tex]\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}[/tex]
1. Samuel's doubling time
[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.055}\\\\& = & \textbf{12.603 yr}\\\end{array}[/tex]
2. Claire's doubling time
[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.05625}\\\\& = & \textbf{12.323 yr}\\\end{array}[/tex]
3. Samuel's doubling time vs Claire's
12.603 - 12.323 = 0.28 yr
It would take 0.28 yr longer for Samuel's money to double than Claire's.
